Problem: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-2x-y &= 1 \\ 3x-6y &= 3\end{align*}$
Solution: Begin by moving the $y$ -term in the second equation to the right side of the equation. $3x = 6y+3$ Divide both sides by $3$ to isolate $x$ $x = {2y + 1}$ Substitute this expression for $x$ in the first equation. $-2({2y + 1}) - y = 1$ $-4y - 2 - y = 1$ Simplify by combining terms, then solve for $y$ $-5y - 2 = 1$ $-5y = 3$ $y = -\dfrac{3}{5}$ Substitute $-\dfrac{3}{5}$ for $y$ in the top equation. $-2x+ \dfrac{3}{5} = 1$ $-2x+\dfrac{3}{5} = 1$ $-2x = \dfrac{2}{5}$ $x = -\dfrac{1}{5}$ The solution is $\enspace x = -\dfrac{1}{5}, \enspace y = -\dfrac{3}{5}$.